Towards Adaptive Subspace Detection in Heterogeneous Environment

In this paper, we aim to take one step forward to the scenario where an adaptive subspace detection framework is required to detect subspace signals in non-stationary environments. Despite the fact that this scenario is more realistic, the existing studies in detection theory mostly rely on homogeneous, or partially homogeneous assumptions in the environments for their design process meaning that the covariance matrices of primary and secondary datasets are exactly the same or different up to a scale factor. In this study, we allow some partial information of the train covariance matrix to be shared with the primary dataset, but the covariance matrix in the primary set can be entirely different in the structure. This is particularly true in radar systems where the secondary set is collected in distinct spatial and time zones. We design a Generalized Likelihood Ratio Test (GLRT) based detector where the noise is multivariate Gaussian and the subspace interference is assumed to be known. The simulation results reveal the superiority of the proposed approach in comparison with conventional detectors for such a realistic and general scenario.